| Jaulent-Miodek族产生的一个完全可积的有限维三次系统 |
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| 引用本文： | 刘春平.Jaulent-Miodek族产生的一个完全可积的有限维三次系统[J].高校应用数学学报(A辑),1993(2). |
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| 作者姓名： | 刘春平 |
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| 作者单位： | 江苏省徐州师范学院数学系 221009 |
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| 摘 要： | 本文研究Jaulent-Miodek族的对易表示,在无反射位势的特征函数表示:即 q=-〈ψ_2,ψ_2〉,r=(Aψ_2,ψ2); (q,r)~T≡f(ψ),ψ≡(ψ_1,ψ_2)~T所诱导的约束条件下,Jaulent-Miodek族的Lax对的空间部分被非线性化为一个完全可积系统(R~(2N),dψ_1∧dψ_2,H=(?)_0),其中(?)_0=i〈Aψ_1,ψ_2〉+1/2〈ψ_1,ψ_2〉〈Aψ_2,ψ_2〉.时间部分的非线性化导出它的N-对合系{(?)_m},相容方程组((?)_0),((?)_m)的对合解被f映为第m个Jaulent-Miodek方程的解。
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| 关 键 词： | 对易表示 Lenard序列 对合解 Hamilton相流 |
A COMPLETELY INTEGRABLE FINITE-DIMENSION CUBIC SYSTEM GENERATED BY THE JAULENT-MIODEK HIERARCHY |
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| Liu Chunping.A COMPLETELY INTEGRABLE FINITE-DIMENSION CUBIC SYSTEM GENERATED BY THE JAULENT-MIODEK HIERARCHY[J].Applied Mathematics A Journal of Chinese Universities,1993(2). |
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| Authors: | Liu Chunping |
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| Abstract: | In this paper, the commutative representation of the Jaulent-Miodek Hierarchy is discussed. Under the constrained condition induced by the eigenfunction expression of the reflectionless potentialthe spatial part of the Lax pair of the Jaulent-Miodek equation is nonlinearized to be a comletely in-tegrable systemwhile the nonlinearization of the time part leads to its N-involutive system {Fm} . The involutive solution of the compatible system (F0). (Fm) is mapped by / into the solution of the m -th Jaulent-Miodek equation. |
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| Keywords: | Commutative Representation Lenard Sequence Involutive Solution Hamiltoni-an Phase-flow |
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